Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in PYTHON3):

Solution:
n = int(input())
li = list(map(int,input().split()))
li2 = li.copy()
so0 = sorted(li)

diffs = dict()
for i in range(len(li)-1):
    diffs[i]= so0[i+1]-so0[i]
soDiffs = sorted(diffs.items(),key=lambda pair: pair[1])
# print(soDiffs)
ma = 0
for idx,diff in soDiffs:
    so= so0.copy()
    d=so[idx]
    c=so[idx+1]
    # print(c,d)
    so.remove(c)
    so.remove(d)
    a,b = so[-2:]
    exp = (a+b)/(c-d)
    # print(exp)
    if exp > ma:
        ma = exp
    else:
        print(ma)
        break